Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

Find the limit or show that it does not exist.

$ \displaystyle \lim_{t \to \infty}\frac{\sqrt{t} + t^2}{2t - t^2} $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Stark Ledbetter

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

02:19

Daniel Jaimes

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 6

Limits at Infinity: Horizontal Asymptotes

Limits

Derivatives

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

0:00

Find the limit or show tha…

00:32

Find the limit if it exist…

01:03

Find the given limit, or s…

02:07

Find the limit.$$\lim …

Find the limit or show th…

01:09

01:06

All right. So we want to find this limit or show that does not exist. Um And as usual, some people like to do low petals rule here or talk about end behavior. Um I think the best way uh to do limits is to use algebra because limits have to exist before um before derivatives do so lumpy tiles rule doesn't make any sense. You may or may not know that already. So this is really big. The top is really big. The bottom is really big or maybe negative. Really big. I can't tell I'm just going to stop things from being big. So I'm going to divide top and bottom by T squared because that's the thing that's getting big the fastest. Okay, so what happens when I do that? Well, T T is like T to the one half. Right. So this is Um won over now. T to the 3/2. If you just use expanded rules. Um you can think of it as teeth. The negative three halves and then write it as 1/2 to the three halves. Okay, Plus T squared over T squared is one divided by um to T over T squared is two over tea and then minus T squared over two squared is one. I'm just going to write this one more time as something slightly different. This three halves is kind of strange. So one over T to the three halves plus one. And why do I want this? Usually don't want fractions infractions, but um, I only need one theorem for something getting big as T gets big one over T gets small, right one divided by a huge number is always going to be really, really small, as the number gets huger and huger, that goes towards zero, that's what that means. Okay, now, I just have that theorem everywhere in here, I have one divided by big number small, raised, the power of three halves is still small, so that limit, the limit of that part is zero, so then the top is zero plus one is one, divided by the bottom is two times this part goes to zero minus one, it's negative. So my answer is negative one, and I think that's the cleanest way to think about a limit like this.

View More Answers From This Book

Find Another Textbook

02:11

The volume of a cuboid is 280cmcube if the length is 8cm and the breadth is …

00:53

In an AP, if a= 5 and d= -3 find a20

00:45

Find the value of k, if r-1 is a factor of 4x³+3²-4x+ k is

00:44

a fair six sided die is thrown. find the probability of getting the followin…

01:08

Esmerelda rents a car from a company that rents cars by the hour. She has to…

01:04

What should be subtracted from thrice the rational number -8/3 to get 5/2 ?P…

01:31

A place P is 82 m above the Sea level and another place is 13 m below the Se…

01:10

If 5a+ib = 15-3i; then find the value of a+bJust the final answer is enough!…

02:08

A book sold for 5.40$ at the profit of 8% on cost price .What is the cost pr…

02:31

If 8x -7y=11 and 7x - 8y =4 ,then what is the value of x+y1.) 12) 73) 154) 4…